Dynamic simulation Direct Dynamics

The issue was addressed in Monte Carlo and Molecular Dynamics simulations directly monitoring water structure and the extent of hydrogen bonding as the molecules became increasingly aligned by the applied field [68]. Below, we report results for fields up to 0.8 V corresponding to actual fields of up to... 

The potential energy function describes the energetic change as a function of the variations in atomic coordinates, including thermal fluctuations and rearrangements of the chemical bonds. The accuracy of the potential energy function used to carry out molecular dynamics simulations directly affects... 

It can be argued that these models are easier to construct, compared to strategies that exploit symmetry operators as described in the first half of this chapter. In particular, one needs only to specify a (crystallisation) temperature and molecular dynamical simulation directs the atoms into appropriate low-energy configurations, which include the evolution of a rich microstructure. However, it can be difficult to ascertain the (simulation) conditions that facilitate crystallisation. 

Barone M E and Graves D B 1995 Molecular dynamics simulations of direct reactive ion etching of silicon by fluorine and chlorine J. Appi. Phys. 78 6604-15... 

For larger systems, various approximate schemes have been developed, called mixed methods as they treat parts of the system using different levels of theory. Of interest to us here are quantuin-seiniclassical methods, which use full quantum mechanics to treat the electrons, but use approximations based on trajectories in a classical phase space to describe the nuclear motion. The prefix quantum may be dropped, and we will talk of seiniclassical methods. There are a number of different approaches, but here we shall concentrate on the few that are suitable for direct dynamics molecular simulations. An overview of other methods is given in the introduction of [21]. 

To add non-adiabatic effects to semiclassical methods, it is necessary to allow the trajectories to sample the different surfaces in a way that simulates the population transfer between electronic states. This sampling is most commonly done by using surface hopping techniques or Ehrenfest dynamics. Recent reviews of these methods are found in [30-32]. Gaussian wavepacket methods have also been extended to include non-adiabatic effects [33,34]. Of particular interest here is the spawning method of Martinez, Ben-Nun, and Levine [35,36], which has been used already in a number of direct dynamics studies. 

By its nature, the application of direct dynamics requires a detailed knowledge of both molecular dynamics and quantum chemistry. This chapter is aimed more at the quantum chemist who would like to use dynamical methods to expand the tools at theh disposal for the study of photochemistry, rather than at the dynamicist who would like to learn some quantum chemishy. It hies therefore to introduce the concepts and problems of dynamics simulations, shessing that one cannot strictly think of a molecule moving along a trajectory even though this is what is being calculated. 

A typical molecular dynamics simulation comprises an equflibration and a production phase. The former is necessary, as the name imphes, to ensure that the system is in equilibrium before data acquisition starts. It is useful to check the time evolution of several simulation parameters such as temperature (which is directly connected to the kinetic energy), potential energy, total energy, density (when periodic boundary conditions with constant pressure are apphed), and their root-mean-square deviations. Having these and other variables constant at the end of the equilibration phase is the prerequisite for the statistically meaningful sampling of data in the following production phase. 

A molecular dynamics simulation nsnally starts with a molecular structure refined by geometry optimization, but wnthont atomic velocities. To completely describe the dynamics of a classical system con lain in g X atom s, yon m nsl define 6N variables. These correspond to ilX geometric coordinates (x, y, and /) and iSX variables for the velocities of each atom in the x, y, and /. directions. 

The forces are calculated as part of a molecular dynamics simulation, cind so little additional effort is required to calculate the virial and thus the pressure. The forces are not routinely calculated during a Monte Carlo simulation, and so some additional effort is required to determine the pressure by this route. When calculating the pressure it is also important to check that the components of the pressure in all three directions are equal. 

The thermodynamic properties that we have considered so far, such as the internal energy, the pressure and the heat capacity are collectively known as the mechanical properties and can be routinely obtained from a Monte Carlo or molecular dynamics simulation. Other thermodynamic properties are difficult to determine accurately without resorting to special techniques. These are the so-called entropic or thermal properties the free energy, the chemical potential and the entropy itself. The difference between the mechanical emd thermal properties is that the mechanical properties are related to the derivative of the partition function whereas the thermal properties are directly related to the partition function itself. To illustrate the difference between these two classes of properties, let us consider the internal energy, U, and the Fielmholtz free energy, A. These are related to the partition function by ... 

Just as one may wish to specify the temperature in a molecular dynamics simulation, so may be desired to maintain the system at a constant pressure. This enables the behavior of the system to be explored as a function of the pressure, enabling one to study phenomer such as the onset of pressure-induced phase transitions. Many experimental measuremen are made under conditions of constant temperature and pressure, and so simulations in tl isothermal-isobaric ensemble are most directly relevant to experimental data. Certai structural rearrangements may be achieved more easily in an isobaric simulation than i a simulation at constant volume. Constant pressure conditions may also be importai when the number of particles in the system changes (as in some of the test particle methoc for calculating free energies and chemical potentials see Section 8.9). 

Once a PES has been computed, it is often fitted to an analytic function. This is done because there are many ways to analyze analytic functions that require much less computation time than working directly with ah initio calculations. For example, the reaction can be modeled as a molecular dynamics simulation showing the vibrational motion and reaction trajectories as described in Chapter 19. Another technique is to fit ah initio results to a semiempirical model designed for the purpose of describing PES s. 

Molecular dynamics simulation, which provides the methodology for detailed microscopical modeling on the atomic scale, is a powerful and widely used tool in chemistry, physics, and materials science. This technique is a scheme for the study of the natural time evolution of the system that allows prediction of the static and dynamic properties of substances directly from the underlying interactions between the molecules. 

In a different context, conformational analysis is essential for the analysis of molecular dynamics simulations. As discussed in Chapter 3, the direct output of a molecular dynamics simulation is a set of confonnations ( snapshots ) that were saved along the trajectory. These conformations are subsequently analyzed in order to extract information about the system. However, if, during a long simulation, the molecule moves from one... 

In thermal building-dynamics simulation codes, outdoor conditions are mostly input by the so-called weather data file, containing (usually hourly) data for air temperature, wind speed and direction, air humidity, and global and diffuse solar radiation on horizontal surfaces. 

In order to run a dynamic simulation, weather data files are needed, providing (usually hourly) data on the following quantities air temperature, air humidity, ground temperature, global and diffuse irradiation on horizontal surfaces, and wind speed and direction. 

P. Zumbusch, W. Kulcke, G. Brunner. Use of alternating electric fields as antifouling strategy in ultrafiltration of biological suspensions. Introduction of a new experimental procedure for crossflow filtration. J Memb Sci 142-.15 (1998). R. L. Rowley, T. D. Shupe, M. W. Schuck. A direct method for determination of chemical potential with molecular dynamics simulations. 1. Pure components. Mol Phys 52 841, 1994. 

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